Abstract

In an earlier paper, we reported that the low-density parity-check (LDPC) codes from finite planes outperform any other known forward error-correction (FEC) scheme for optical communications. However, the number of different LDPC codes of code rate above 0.8 is rather small. As a natural extension of the prior work, in this paper, we consider LDPC codes on m flats derived from projective and affine geometries, which outperform codes from finite planes. The codes on m flats also provide a greater selection of structured LDPC codes of rate 0.8 or higher. The performance of the codes in a long-haul optical-communication system was assessed using an advanced simulator able to capture all important transmission impairments. Specifically, they achieve a coding gain of 10 dB at a bit error rate (BER) of 10-9, outperforming, therefore, the best turbo product codes proposed for optical communications. In addition, the simulator implements a fixed-point (FP) iterative decoder that allows control of the precision of the soft information used in the decoder. Such quantization is required to facilitate hardware implementations of the iterative decoder, and the high-speed operations for long-haul optical transmission systems. The loss in performance due to reduced precision of the soft information can be as low as 0.2 dB.

© 2005 IEEE

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  2. I. B. Djordjevic, S. Sankaranarayanan and B. Vasic, "Irregular low-density parity-check codes for long haul optical communications", IEEE Photon. Technol. Lett., vol. 16, no. 1, pp. 338-340, Jan. 2004.
  3. I. B. Djordjevic and B. Vasic, "MacNeish-Mann theorem based iteratively decodable codes for optical communication systems", IEEE Commun. Lett., vol. 8, no. 8, pp. 538-540, Aug. 2004.
  4. I. B. Djordjevic and B. Vasic, "High code rate low-density parity-check codes for optical communication systems", IEEE Photon. Technol. Lett., vol. 16, no. 6, pp. 1600-1602, Jun. 2004.
  5. O. Milenkovic, I. B. Djordjevic and B. Vasic, "Block-circulant low-density parity-check codes for optical communication systems", IEEE/LEOS J. Sel. Topics Quantum Electron., vol. 10, no. 2, pp. 294-299, Mar./Apr. 2004.
  6. T. Richardson, A. Shokrollahi and R. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes", IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 619-637, Feb. 2001.
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  31. F. Lustenberger, "On the design of analog VLSI iterative decoders", Ph.D. thesis, Swiss Federal Inst. Technol., Zurich, Switzerland, Nov. 2000.
  32. D. Chase, "A class of algorithms for decoding of block codes with channel measurements information", IEEE Trans. Inf. Theory, vol. IT-18, no. 1, pp. 170-179, Jan. 1972.
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Other (35)

I. B. Djordjevic, S. Sankaranarayanan and B. Vasic, "Projective plane iteratively decodable block codes for WDM high-speed long-haul transmission systems", J. Lightw. Technol., vol. 22, no. 3, pp. 695-702, Mar. 2004.

I. B. Djordjevic, S. Sankaranarayanan and B. Vasic, "Irregular low-density parity-check codes for long haul optical communications", IEEE Photon. Technol. Lett., vol. 16, no. 1, pp. 338-340, Jan. 2004.

I. B. Djordjevic and B. Vasic, "MacNeish-Mann theorem based iteratively decodable codes for optical communication systems", IEEE Commun. Lett., vol. 8, no. 8, pp. 538-540, Aug. 2004.

I. B. Djordjevic and B. Vasic, "High code rate low-density parity-check codes for optical communication systems", IEEE Photon. Technol. Lett., vol. 16, no. 6, pp. 1600-1602, Jun. 2004.

O. Milenkovic, I. B. Djordjevic and B. Vasic, "Block-circulant low-density parity-check codes for optical communication systems", IEEE/LEOS J. Sel. Topics Quantum Electron., vol. 10, no. 2, pp. 294-299, Mar./Apr. 2004.

T. Richardson, A. Shokrollahi and R. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes", IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 619-637, Feb. 2001.

D. MacKay and M. Davey, "Evaluation of Gallager Codes for Short Block Length and High Rate Applications",

J. Hagenauer, M. Moerz and E. Offer, "Analog turbo-networks in VLSI: The next step in turbo decoding and equalization", in Proc. 2nd Int. Symp. Turbo Codes, Brest, France,Sep. 4-7 2000, pp. 209-218.

Y. Kou, S. Lin and M. P. C. Fossorier, "Low-density parity-check codes based on finite geometries: A rediscovery and new results", IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 2711-2736, Nov. 2001.

S. R. Weller and S. J. Johnson, "Iterative decoding of codes from oval designs", presented at the Defense Applications of Signal Processing, Workshop (DASP), Adelaide, S.A., Australia,Sep. 16-20, 2001.

J. Hagenauer, E. Offer and L. Papke, "Iterative decoding of binary block and convolutional codes", IEEE Trans. Inf. Theory, vol. 42, no. 2, pp. 429-445, Mar. 1996.

E. Yeo, B. Nikolic and V. Anantharam, "Iterative decoder architectures", IEEE Commun. Mag., vol. 41, no. 8, pp. 132-140, Aug. 2003.

H. Xiao-Yu, E. Eleftheriou, D.-M. Arnold and A. Dholakia, "Efficient implementations of the sum-product algorithm for decoding LDPC codes", in Proc. Global Telecommunications (GLOBECOM), vol. 2, San Antonio, TX, Nov. 2001, pp. 1036-1036E.

K. Azadet, E. F. Haratsch, H. Kim, F. Saibi, J. H. Saunders, M. Shaffer, L. Song and Y. Meng-Lin, "Equalization and FEC techniques for optical transceivers", IEEE J. Solid-State Circuits, vol. 37, no. 3, pp. 317-327, Mar. 2002.

O. A. Sab, "FEC techniques in submarine transmission systems", in Proc. Optical Fiber Communication Conf., vol. 2, Anaheim, CA, 2001, pp. TuF1-1-TuF1-3.

O. A. Sab and V. Lemarie, "Block turbo code performances for long-haul DWDM optical transmission systems", in Proc. Optical Fiber Communication Conf., vol. 3, Anaheim, CA, 2001, pp. 280-282.

T. Mizuochi, et al. "Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems", IEEE J. Sel. Topics Quantum Electron., vol. 10, no. 2, pp. 376-386, Mar./Apr. 2004.

I. B. Djordjevic and B. Vasic, "Projective geometry low-density parity-check codes for ultra-long haul WDM high-speed transmission", IEEE Photon. Technol. Lett., vol. 15, no. 5, pp. 784-786, May 2003.

B. Vasic, I. B. Djordjevic and R. Kostuk, "Low-density parity check codes and iterative decoding for long haul optical communication systems", J. Lightw. Technol., vol. 21, no. 2, pp. 438-446, Feb. 2003.

B. Vasic and I. B. Djordjevic, "Low-density parity check codes for long haul optical communications systems", IEEE Photon. Technol. Lett., vol. 14, no. 8, pp. 1208-1210, Aug. 2002.

B. Vasic and O. Milenkovic, "Combinatorial constructions of structured low-density parity check codes for iterative decoding", IEEE Trans. Inf. Theory, vol. 50, no. 6, pp. 1156-1176, Jun. 2004.

H. Tang, J. Xu, S. Lin and K. Abdel-Ghaffar, "Codes on finite geometries", IEEE Trans. Inf. Theory, vol. 51, no. 2, pp. 572-596, Feb. 2005.

I. B. Djordjevic and B. Vasic, "An advanced direct detection receiver model", J. Opt. Commun., vol. 25, no. 1, pp. 6-9, Feb. 2004.

I. F. Blake and R. C. Mullin, The Mathematical Theory of Coding, New York: Academic, 1975.

W. E. Ryan, "An introduction to LDPC codes," in CRC Handbook for Coding and Signal Processing for Recording Systems, B. Vasic, Ed. Boca Raton, FL: CRC, 2004.

E. F. Assmus Jr. and J. D. Key, "Baer subplanes, ovals and unitals," in Coding Theory and Design Theory, Part I, D. Ray-Chaudhuri Ed. New York: Springer-Verlag, 1990,vol. 20, pp. 1-8.

E. F. Assmus Jr. and J. D. Key, Designs and Their Codes, Cambridge: U.K.: Cambridge Univ. Press, 1992.

E. F. Assmus Jr. and J. D. Key, "Designs and codes: An update", Designs, Codes Cryptogr., vol. 9, no. 1, pp. 7-27, Aug. 1996.

G. P. Agrawal, Nonlinear Fiber Optics, San Diego, CA: Academic, 2001.

G. Montorsi and S. Benedetto, "Design of fixed-point iterative decoders for concatenated codes with interleavers", IEEE J. Sel. Areas Commun., vol. 19, no. 5, pp. 871-882, May 2001.

F. Lustenberger, "On the design of analog VLSI iterative decoders", Ph.D. thesis, Swiss Federal Inst. Technol., Zurich, Switzerland, Nov. 2000.

D. Chase, "A class of algorithms for decoding of block codes with channel measurements information", IEEE Trans. Inf. Theory, vol. IT-18, no. 1, pp. 170-179, Jan. 1972.

S. A. Hirst, B. Honary and G. Markarian, "Fast chase algorithm with an application in turbo decoding", IEEE Trans. Commun., vol. 49, no. 10, pp. 1693-1699, Oct. 2001.

W. E. Ryan, "Concatenated convolutional codes and iterative decoding," in Wiley Encyclopedia in Telecommunications, J. G. Proakis, Ed. New York: Wiley, 2003.

M. Mansour, "Implementation of LDPC decoders", presented at the IEEE Communications Theory Workshop, Park City, UT, Jun. 13-15, 2005.

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